Mathematics
Grade 8
15 min
Probability of simple events
Probability of simple events
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1
Introduction & Learning Objectives
Learning Objectives
Define key probability terms such as outcome, event, sample space, and simple event.
Identify the sample space and favorable outcomes for a given simple event.
Calculate the theoretical probability of a simple event.
Calculate the experimental probability of a simple event based on given data.
Express probabilities as fractions, decimals, and percentages.
Interpret probability values, understanding what probabilities of 0, 1, and values in between signify.
Apply probability concepts to real-world scenarios involving simple events.
Ever wonder what your chances are of winning a game or if it will rain tomorrow? 🎲 Probability helps us understand the likelihood of things happening!
In this lesson, you'll learn how to measure the chance of a single e...
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Key Concepts & Vocabulary
TermDefinitionExample
ProbabilityA measure of how likely an event is to occur. It's a number between 0 and 1, where 0 means impossible and 1 means certain.The probability of flipping a coin and getting heads is 1/2.
OutcomeA single possible result of an experiment or situation.When rolling a standard six-sided die, 'rolling a 3' is an outcome.
EventA specific outcome or a set of outcomes that you are interested in.When rolling a die, 'rolling an even number' is an event, which includes the outcomes {2, 4, 6}.
Sample SpaceThe set of all possible outcomes of an experiment.For rolling a standard six-sided die, the sample space is {1, 2, 3, 4, 5, 6}.
Simple EventAn event that consists of only one outcome from the sample space.When flipping a coin, 'getting tails&...
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Core Formulas
Theoretical Probability Formula
$$P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$
This formula is used to calculate the probability of an event when all outcomes in the sample space are equally likely. 'Favorable outcomes' are the outcomes that satisfy the event you are interested in.
Experimental Probability Formula
$$P(\text{Event}) = \frac{\text{Number of times the event occurred}}{\text{Total number of trials}}$$
This formula is used to calculate probability based on actual observations or experiments. 'Trials' refer to the number of times the experiment was performed.
Probability Range Rule
$$0 \le P(\text{Event}) \le 1$$
The probability of any event must be a number between 0 and 1, in...
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Challenging
A bag contains only red, blue, and green marbles. The probability of picking a red marble is 1/4, and the probability of picking a blue marble is 1/3. What is the probability of picking a green marble?
A.5/12
B.7/12
C.1/2
D.2/3
Challenging
A student is asked to find the probability of picking a consonant from the word 'APPLE'. They reason: 'There are 3 unique consonants (P, L) and 2 unique vowels (A, E), so the probability is 3/2.' Which critical error did the student make?
A.They misidentified the sample space.
B.They calculated P(Vowel) instead of P(Consonant).
C.Their probability is greater than 1.
D.They did not simplify the fraction.
Challenging
A game has a spinner with sections of different sizes. The blue section covers half the spinner, and the red section covers the other half. Why is the formula P(Event) = (Number of favorable outcomes) / (Total number of possible outcomes) misleading here if we define outcomes as 'blue' and 'red'?
A.The formula only works for dice.
B.The formula assumes all outcomes are equally likely.
C.The total number of outcomes is unknown.
D.The spinner could land on a line.
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